Magnetic dipole moment of current carrying circular coil is ...... length of wire of coil.

Options

A. directly proportional
B. directly proportional to square root of
C. inversely proportional to square of
D. directly proportional to square of

Answer

C

Explanation

Dipole moment,
`m= NIA = NI (pi r^(2) )`
But length of wire,
`l=2pi r`
`therefore r=(l)/(2pi)`
`therefore r^(2) = (l^2)/(4pi^(2) )`
`therefore m= NI xx pi xx (l^2)/( 4pi^(2) )`
`therefore` In `m= (Nil^(2) )/(4pi ) , (NI)/(4pi)` is constant.
`therefore m prop l^(2) therefore` Option (C) is correct.